A reflex loudspeaker enclosure is one in which the rear of a loudspeaker diaphragm radiates into an enclosed air volume, with a duct known as a ‘port tube’ connecting this air volume to free space.
The port tube and the enclosed volume combine to behave as a Helmholtz resonator which, when driven by the rear of the loudspeaker diaphragm, results in a fourth order high pass response at low frequencies. This system provides greater low frequency output in the region of the port tuning frequency.
The alignment of this type of loudspeaker has been well documented by Neville Thiele (see for example Thiele, A. N., “Loudspeakers in Vented Boxes, Parts I and II”, J. Audio Eng. Soc., vol. 19, pp. 382-392 (May 1971); pp. 471-483 (June 1971)) and Richard Small (see for example “Vented-Box Loudspeaker Systems”, J. Audio Eng. Soc., vol. 21, pp. 363-372 (June 1973); pp. 438-444 (July/August 1973); pp. 549-554 (September 1973); pp. 635-639 (October 1973)).
The tuning frequency of the port is given by the well known equation derived for a Helmholtz resonator. That is,
                                          f            H                    =                                    v                              2                ⁢                π                                      ⁢                                          A                                                      V                    0                                    ⁢                  L                                                                    ,                            (        1        )            where fH is the Helmholtz resonant frequency, ν is the speed of sound through the atmosphere, A is the cross-sectional area of the port, V0 is the static volume of the port and L is the length of the port. A particular tuning frequency may be achieved therefore with a short port of small area or a longer port of correspondingly larger area.
However, the sound pressure within the box results in waves travelling down the port. These are reflected by the large change of acoustic impedance at the ends of the tube, resulting in longitudinal resonances similar to those found in organ tubes and many other musical instruments. These resonances produce undesirable peaks in the acoustic output of the port which distort the tonal purity of the loudspeaker. In some cases visible anomalies are produced in the frequency response of the loudspeaker. This effect is extremely undesirable in a high quality loudspeaker.
In practice, air flow in the port is also a significant issue since at high velocities turbulence may occur (A. Salvatti, A. Devantier and D. J. Button, “Maximizing Performance from Loudspeaker Ports,” J. Audio Eng. Soc, vol. 50, no. 1/2, pp. 19-45, 2002.). Turbulence causes distortion and loss of output so is best avoided at working levels.
FIG. 1 shows the calculated frequency responses of a driven diaphragm, a reflex port, and their combination in a conventional reflex loudspeaker. The goal of high-performance loudspeakers is to achieve as smooth and even a response as possible across the range of working frequencies of the device. It can be seen that, on its own, the diaphragm displays a response which is both smooth and at a good level at higher frequencies but drops off markedly at lower frequencies. The reflex port is designed to counteract this low-frequency drop off, and provides a relatively high response at low frequencies (corresponding to Helmholtz resonance) and a low response at high frequencies. Thus, their combination leads to a response that is more extended at low frequencies than for the diaphragm alone.
However, the reflex port also exhibits a number of sharp peaks in its response at high frequencies, corresponding to the longitudinal-mode resonances described above. This in turn leads to peaks in the response of the loudspeaker as a whole and undesirable distortion of the projected sound.